Heat oven to 400°F (205℃). Butter a large casserole dish or 9x13 inch pan. Pat chicken thighs dry with a paper towel and season and all sides with salt and pepper.
Heat olive oil in a Dutch oven or deep skillet (with lid) over medium heat. Add chicken thighs, skin side down and cook for 5-6 minutes, or until skin is nicely browned and a good amount of fat has rendered into the pan. Flip and sear the meat side for about 1 minute. Remove to a plate.
Add onions and garlic to skillet and cook briefly until fragrant. Add greens and cook while stirring until wilted, 2-3 minutes. Mix in chicken stock, ½ tsp salt, ¼ tsp pepper. Place chicken thighs skin side up on top of greens. Cover and transfer to oven for 25 minutes.
Meanwhile, bring a large pot of salted water to boil over high heat and cook pasta per package directions for al dente. (More al dente is better, it will continue to cook in the oven). Drain and return to pot.
When chicken thighs are done cooking, transfer them to a cutting board. Transfer the rest of the Dutch oven contents into a blender. Add Greek yogurt or sour cream and blend until smooth.
Remove bones from chicken thighs and cut the meat into bite-sized chunks. Add chicken to the pot of pasta, along with green sauce, and 1½ cups mozzarella cheese. Mix to combine.
Spread pasta into an even layer in the buttered dish. Top with remaining mozzarella cheese. Bake for 25-30 minutes or until cheese is melted and starting to brown. Allow to sit for 10 minutes before slicing and serving. Top with desired toppings.